Optimization design model construction of round faceted gemstone facets based on geometric transformation theory

The current gemstone jewelry design is not specialized and systematic enough, and most of the gemstone jewelry styles are common and single, which makes the value of gemstone not reasonably reflected. Starting from the evolution of gemstone facets, facet texture and cut classification, the article takes the three-dimensional features of gemstone facets as the basis and optimizes the cut parameters of gemstone facets by combining with geometric transformation theory. The optimized cutting parameters were used as the basis for 3D modeling, and the 3D model of the round faceted gemstone facets was established with the simulation software, and the quantitative analysis of the data was carried out through the brightness, uniformity, and scintillation values. When the table width ratio is 50-60%, the difference between the crown angle and the inclination angle of the star facet corresponding to the circular faceted gemstone facets varies from 9.172° to 20.673°. When the length ratio of the lower girdle facets is 65% to 95%, respectively, the range of the difference between the lower girdle facet inclination and the pavilion angle is between 0.781° and 1.967°. The scintillation value obtained after designing the gem facets using the method of this paper is 4.67 times higher than that of the traditional method. The optimized design model of round faceted faceted gemstones constructed on the basis of geometric transformation theory can provide new ideas for the jewelry design of round faceted faceted gemstones.